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Molecular Modeling of Surfactant Micellization Using Solvent Accessible Surface Area Hsieh Chen, and Athanassios Z. Panagiotopoulos Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b03440 • Publication Date (Web): 09 Jan 2019 Downloaded from http://pubs.acs.org on January 14, 2019

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Molecular Modeling of Surfactant Micellization Using Solvent Accessible Surface Area Hsieh Chen1,* and Athanassios Z. Panagiotopoulos2 1Aramco

Services Company: Aramco Research Center – Boston, 400 Technology Square, Cambridge,

MA 02139 2Department

of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08544

*[email protected]

1 ACS Paragon Plus Environment

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ABSTRACT We report a new implicit-solvent simulation model for studying the self-assembly of surfactants, where the hydrophobic interactions were captured by calculating the relative changes of the solvent accessible surface area (SASA) of the hydrophobic domains. Using histogram-reweighting grand canonical Monte Carlo simulations, we demonstrate that this approach allows us to match both the experimental critical micelle concentrations (cmc) and micellar aggregation numbers simultaneously with a single phenomenological surface tension γSASA for the poly(oxyethylene) monoalkyl ether (CmEn) surfactants in aqueous solutions. Excellent transferability is observed: the same model can accurately predict the experimental cmc and aggregation numbers for the CmEn surfactants with alkyl lengths m between 6 and 12, and poly(oxyethylene) lengths n between 1 and 9. The SASA-based implicit-solvent model put forward in this work is general and may be applied to study more complex amphiphilic systems such as surfactants with branched alkyl chains, or surfactant-hydrocarbon mixtures.


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INTRODUCTION Surfactants are present in a large number of industrial applications, including detergency, catalysis, pharmaceutical, food, cosmetic, materials synthesis, nanotechnology, and tertiary oil recovery.17

In nature, lipids are the most important components of biological cell membranes and are involved in

multiple biochemistry processes.8, 9 The key features of the surfactant molecules are their ability to selfassemble into a variety of nanostructures, such as spherical and cylindrical micelles, hexagonal phases, cubic phases, and lamellae. Moreover, their morphologies are usually controllable by the different surfactant molecular architectures, concentrations, temperatures, solvent types, co-surfactants, and the presence of salts or other solutes.10-12 Because of its importance as well as its complexity, micellization in surfactant solutions has been extensively studied by experiments,13-17 theories,18-23 and computer simulations.24-34 Molecule-based simulations are particularly useful in providing direct links between the molecular scale interactions and the diverse self-assembly behaviors. Explicit-solvent molecular dynamics simulations have been widely used to study the structural properties, water penetration, and counterion bindings of (usually preassembled) micelles.35-42 However, due to computational limitations, it has been difficult to simulate micellization processes using explicit-solvent models.43-46 Typical micellization time scales (>1 μs)47 can only be reached through extensive simulations. Even worse, micellization usually occurs at low concentrations ( 300 before the termination of the specific simulation run, indicating phase separation instead of micellization of the surfactants.

CONCLUSIONS In this work, we have demonstrated that calculating the surface tensions associated with the hydrophobic solvent accessible surface area (SASA) is a suitable approach for capturing the hydrophobic interactions in surfactant micellization. Specifically, we applied the model to study the nonionic poly(oxyethylene) ether surfactant systems CmEn, with m denoting the hydrophobic alkyl chain lengths and n denoting the hydrophilic poly(oxyethylene) chain lengths. We first adjusted the surface tension 9 ACS Paragon Plus Environment

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γSASA to match the critical micelle concentration (cmc) and micellar aggregation number (M) of the C8E6 surfactants. Encouragingly, both cmc and M matched the experimental values with the same γSASA/kB = 32.5 K/Å2 (γSASA = 65 cal/mol/Å2), which is a realistic value in between the reported microscopic (28-47 cal/mol/Å2) and macroscopic (72-75 cal/mol/Å2) hydrocarbon-water interface tensions. We then used the optimized γSASA to predict the cmc and M for the different CmEn surfactants with varied m = 6 to 12 and n = 1 to 9, and found very good agreements with the respective experimental values, indicating excellent transferability of the present method. Finally, we investigated the snapshots of the isolated micellar aggregates from simulations and found spherical micelles for the C6E6, C8E6, and C8E9 systems; ellipsoidal micelles for the C8E3, C10E6, and C12E6 systems; and the phase separated sheet aggregate for the C8E1 system. The observations of the different micellar shapes were consistent with prior theories and simulations, which highlighted the validity and generality of the new implicit-solvent surfactant model put forward in this work. Even though in this work we have mainly focused on nonionic surfactants, the SASA-based model may be readily generalized to study ionic surfactants as well, since the SASA-based hydrophobic tail bead interaction is agnostic to the surfactant head groups. We then would only need to acquire the parameters for new head groups without modifying SASA parameters. Previously, we have developed an implicit-solvent molecular model for electrolytes based on the concept of concentration dependent dielectric permittivity, which was demonstrated to precisely capture the thermodynamic properties of concentrated electrolytes and their mixtures.66 We believe the same method may be applied to describe the charged head groups of the ionic surfactants; further, we may combine the surfactant and electrolyte models to study the ion-specific effects in micellization. A final point relates to the temperature-dependent properties. In this work, we have obtained the optimized γSASA at T = 298.15 K. Nevertheless, it has been known that the water-hydrocarbon interface tension is a non-linear function of temperature, which is governed by the collective hydration behavior.109, 110

The temperature-dependent properties may be captured by first obtaining γSASA(T) either by adjusting it 10 ACS Paragon Plus Environment

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at different temperatures, or by applying other analytical corrections. With optimal γSASA(T), we expect our model can also be used to capture the temperature driven phenomena such as the cloud points for the CmEn surfactants. Further studies in this area are needed to validate the aforementioned approaches.

ACKNOWLEDGEMENTS We thank Aramco Research Center-Boston, Reservoir Engineering Technology team members for valuable discussions. We acknowledge ASC, IT Services for managing computational resources.

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Figure 1. Schematic illustration that the hydrophobic interactions were captured from the surface tensions associated with the hydrophobic solvent accessible surface area (SASA).


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Figure. 2. (A) Osmotic pressure (Π = P) versus concentration (c = N/V) curves, and (B) aggregate size distributions (with M denoting micellar aggregation numbers) for the C8E6 surfactants with different γSASA. The black line in (A) corresponds to ideal solutions.


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Figure. 3. (A) Critical micelle concentrations (cmc) and (B) micellar aggregation numbers (M) as a function of γSASA for the C8E6 surfactants from implicit-solvent GCMC simulations (black squares). Experimental values from Ref. 50 are shown as red dashed lines.


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Figure 4. (A) Critical micelle concentrations (cmc) and (B) micellar aggregation numbers (M) for the CmE6 surfactants from implicit-solvent GCMC simulations (black squares) and from experiments (red triangles).50, 104 The red dashed line in (A) is an exponential fit for the experimental results. Error bars are only shown if larger than the symbols.


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Figure 5. (A) Critical micelle concentrations (cmc) and (B) micellar aggregation numbers (M) for the C8En surfactants from implicit-solvent GCMC simulations (black squares) and from experiments (red triangles).50, 105, 106 The red dashed line in (A) is a linear fit for the experimental results. Error bars are only shown if larger than the symbols.


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Figure 6. Snapshots of the isolated micelles from the different CmEn surfactant systems studied in this work. The hydrophobic beads are shown in cyan, and the hydrophilic beads are shown in orange.


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Figure 7. Snapshots of the phase separated C8E1 surfactant aggregate. The bead colors are the same as in Fig. 6.


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